The legislative committee investigating the George Washington Bridge lane closures is fighting to require two ex-aides to Gov. Chris Christie to provide records related to the matter, arguing in court papers that they can’t wave away subpoenas previously issued to them.

Bridget Kelly and Bill Stepien, the two former aides to Mr. Christie, are seeking to exercise their Constitutional right against self-incrimination in an effort to avoid turning over documents to the New Jersey committee.

In a 35-page brief sent to the court Friday, the committee’s counsel pushed back specifically on arguments presented by Mr. Stepien’s attorney, Kevin Marino, in legal papers filed earlier in the week. Mr. Marino had argued that Mr. Stepien was innocent and that his Fifth Amendment privileges extend beyond testimony to include records.

“Mr. Stepien cannot escape compliance with the subpoena simply by offering a blanket claim of privilege and asserting he is an ‘innocent man,’” wrote lawyers with Sokol, Behot & Fiorenzo, the Hackensack-based firm that is representing the committee along with a former U.S. Attorney.

New Jersey lawmakers have issued 38 subpoenas for additional records pertaining to the closures. The bipartisan committee is investigating whether the September lane closures were orchestrated to settle possible political vendettas. The five days of lane closures caused traffic gridlock in Fort Lee, N.J., at the western end of the bridge.

Ms. Kelly and Mr. Stepien are the only two individuals who are fighting the subpoenas. A court case to consider the matter is slated to be held in Superior Court in Mercer County Tuesday.

In papers submitted earlier in the week, attorneys representing Mr. Stepien and Ms. Kelly argued that Democrats on the committee had prejudiced the investigation in statements and appearing on television programs speaking about the case. They particular singled out Democratic Assemblyman John Wisniewski, the committee’s co-chair.

The committee’s lawyers dismissed that argument, saying that Mr. Wisniewski is a lawmaker, not a law enforcement official.

“Chairman Wisniewski is not a prosecutor and the committee is not a grand jury,” the attorneys wrote. “Chairman Wisniewski’s statements and opinions are just that—his statements and opinions.”

The committee’s counsel also argued that Mr. Stepien’s refusal to comply with the subpoenas across the board would dilute the power of investigators to look into any matter.

“If Mr. Stepien is correct, this would all but destroy government investigations,” they wrote. “The committee’s subpoena requests are wholly lawful and constitutional.”